While it has been realized for quite some time within AI that abduction is a general model of explanation for a variety of tasks, there have been no empirical investigations into the practical feasibility of a general, logic-based abductive approach to explanation. In this paper we present extensive empirical results on applying a general abductive system, ACCEL, to moderately complex problems in plan recognition and diagnosis. In plan recognition, ACCEL has been tested on 50 short narrative texts, inferring characters' plans from actions described in a text. In medical diagnosis, ACCEL has diagnosed 50 real-world patient cases involving brain damage due to stroke (previously addressed by set-covering methods). ACCEL also uses abduction to accomplish model-based diagnosis of logic circuits (a full adder) and continuous dynamic systems (a temperature controller and the water balance system of the human kidney). The results indicate that general purpose abduction is an effective and efficient mechanism for solving problems in plan recognition and diagnosis.